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August 12th, 2015, 08:02 AM  #1 
Newbie Joined: Dec 2010 Posts: 19 Thanks: 0  How many triangles in this picture?
Hi, all. I just thought of that kind of question and tried to count it. Please see the picture below. Finally got 42. Can anyone help me confirm the answer, please? Thank you very much. Last edited by Kavesat; August 12th, 2015 at 08:04 AM. 
August 12th, 2015, 08:37 AM  #2 
Senior Member Joined: Feb 2010 Posts: 682 Thanks: 129 
I think I agree ... 42. Call the lower left vertex A and the lower right vertex B. Then there are 30 triangles with A as vertex, 24 triangles with B as vertex and 12 triangles with AB as a side (that is, both A and B as vertices). By the inclusionexclusion principle the total is 30 + 24  12 = 42. 
August 12th, 2015, 09:18 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 19,167 Thanks: 1639 
42


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